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Q4. Consider the topological space (X,T), where X = {a, b, c, d) and T = { 0, X, {a}, {b}, {c}, {a,b}, {a, c}, {b,c}, {a,b,c}}. (a) Is (X, T) a Hausdorff space? Justify your answer. (b) Is (X, T) a regular space? Why? (c) Is (X, T) a normal space? Why?

Q4. Consider the topological space (X,T), where X = {a, b, c, d) and T = { 0, X, {a}, {b}, {c}, {a,b}, {a, c}, {b,c}, {a,b,c}}. (a) Is (X, T) a Hausdorff space? Justify your answer. (b) Is (X, T) a regular space? Why? (c) Is (X, T) a normal space? Why?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q4. Consider the topological space (X,T), where X = {a, b, c, d} and T = { ¢, X, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}. (a) Is (X,T) a Hausdorff space? Justify your answer. (b) Is (X,T) a regular space? Why? (c) Is (X, T) a normal space? Why?
Transcribed Image Text:Q4. Consider the topological space (X,T), where X = {a, b, c, d} and T = { ¢, X, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}. (a) Is (X,T) a Hausdorff space? Justify your answer. (b) Is (X,T) a regular space? Why? (c) Is (X, T) a normal space? Why?
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